The characteristic linear dimension is given as a certain combination of
the three most fundamental constants of nature: (1) Planck's constant h
(named after the German physicist Max Planck, the founder of quantum
physics), (2) the speed of light c, and (3) the universal gravitational
constant G. The combination, called the Planck length (Gh/c3)1/2,
equals roughly 10-33 cm, far smaller than the distances to which
elementary particles can be probed in particle accelerators on the Earth.

The energies needed to smash particles to within a Planck length of each
other were available to the universe at a time equal to the Planck length
divided by the speed of light. This time, called the Planck time
(Gh/c5)1/2, equals approximately 10-43 second. At the
Planck time, the mass density of the universe is thought to approach the
Planck density, c5/hG2, roughly 1093 g/cc . Contained within a
Planck volume is a Planck mass (hc/G)1/2, roughly
10-5 g. An object of such mass would be a quantum black hole,
with an event horizon close to both its own Compton length (distance over
which a particle is quantum mechanically "fuzzy") and the size of the
cosmic horizon at the Planck time. Under such extreme conditions,
spacetime cannot be treated as a classical continuum and must be given a
quantum interpretation.

The latter is the goal of the supergravity theory, which has as one of its
features the curious notion that the four spacetime dimensions (three
space dimensions plus one time dimension) of the familiar world may be an
illusion. Real spacetime, in accordance with this picture, has 26 or 10
spacetime dimensions, but all of these dimensions except the usual four
are somehow compacted or curled up to a size comparable to the Planck
scale. Thus has the existence of these other dimensions escaped
detection. It is presumably only during the Planck era, when the usual
four spacetime dimensions acquire their natural Planck scales, that the
existence of what is more fundamental than the usual ideas of mass-energy
and spacetime becomes fully revealed. Unfortunately, attempts to deduce
anything more quantitative or physically illuminating from the theory have
bogged down in the intractable mathematics of this difficult subject. At
the present time superstring theory remains more of an enigma than a
solution.